Practical Operations Management
2nd Edition
ISBN: 9781939297136
Author: Simpson
Publisher: HERCHER PUBLISHING,INCORPORATED
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Chapter 5, Problem 18P
Summary Introduction
Interpretation: System utilization, considering M/M/1 model.
Concept introduction: The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in an FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further, if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise, it tends to be too variable of a distribution.
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The dry cleaning station has three cleaning devices, r = 3. The intensity of the flow of visitors λ = 6 (person / h). Intensity of serving visitors with one device µ = 3 (person / h). The average number of visitors leaving the queue without waiting for service, ν = 1 (person / hour). Find the absolute throughput of the dry cleaning point.
A bank has 1 enquiries staff and six tellers. Customers enter the system and walk up to the enquires counter for the enquiries queue or they go to the tellers station where they join a single queue for the 6 tellers.The arrival rate at the enquiry counter, lambda 8 customers per hour and the service rate at the enquiry counter, Mu 6 minutes per customer. The arrival rate at the tellers’stations, lambda 10 clients per hour and the service rate at the tellerstations, Mu 4 minutes per client.
Find the total time customers spend at the bank
The office has a single line for customers waiting for the next available clerk. There are two clerks who work at the same rate. On average customers arrive every 8 minutes and the average service rate is 5 per hour for each of the two clerks. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution.
b.) What proportion of time are both clerks idle?
c.) Counting each person being served and the people in line, on average, how many customers would be in this system?
Chapter 5 Solutions
Practical Operations Management
Ch. 5 - Prob. 1DQCh. 5 - Prob. 2DQCh. 5 - Prob. 3DQCh. 5 - Prob. 4DQCh. 5 - Prob. 5DQCh. 5 - Prob. 6DQCh. 5 - Prob. 7DQCh. 5 - Prob. 1PCh. 5 - Prob. 2PCh. 5 - Prob. 3P
Ch. 5 - Prob. 4PCh. 5 - Prob. 5PCh. 5 - Prob. 6PCh. 5 - Prob. 7PCh. 5 - Prob. 8PCh. 5 - Prob. 9PCh. 5 - Prob. 10PCh. 5 - Prob. 11PCh. 5 - Prob. 12PCh. 5 - Prob. 13PCh. 5 - Prob. 14PCh. 5 - Prob. 15PCh. 5 - Prob. 16PCh. 5 - Prob. 17PCh. 5 - Prob. 18PCh. 5 - Prob. 19PCh. 5 - Prob. 20PCh. 5 - Prob. 21PCh. 5 - Prob. 22PCh. 5 - Prob. 23PCh. 5 - Prob. 24PCh. 5 - Prob. 25PCh. 5 - Prob. 26PCh. 5 - Prob. 27PCh. 5 - Prob. 28PCh. 5 - Prob. 29PCh. 5 - Prob. 30PCh. 5 - Prob. 31PCh. 5 - Prob. 32PCh. 5 - Prob. 33PCh. 5 - Prob. 34PCh. 5 - Prob. 35PCh. 5 - Prob. 36PCh. 5 - Prob. 37PCh. 5 - Prob. 38PCh. 5 - Prob. 1.1QCh. 5 - Prob. 1.2QCh. 5 - Prob. 1.3QCh. 5 - Prob. 1.4QCh. 5 - Prob. 2.1QCh. 5 - Prob. 2.2QCh. 5 - Prob. 2.3QCh. 5 - Prob. 3.1QCh. 5 - Prob. 3.2QCh. 5 - Prob. 3.3QCh. 5 - Prob. 3.4Q
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